Periodic plasmonic nanoantennas in a piecewise homogeneous background

Periodic rectangular gold nanomonopoles and nanodipoles in a piecewise inhomogeneous background, consisting of a silicon substrate and a dielectric (aqueous) cover, have been investigated extensively via 3D finite-difference time-domain simulations. The transmittance, reflectance and absorptance response of the nanoantennas were studied as a function of their geometry (length, width, thickness, gap) and found to vary very strongly. The nanoantennas were found to resonate in a single surface plasmon mode supported by the corresponding rectangular cross-section nanowire waveguide, identified as the sa(b)(0) mode [Phys. Rev. B 63, 125417 (2001)]. We determine the propagation characteristics of this mode as a function of nanowire cross-section and wavelength, and we relate the modal results to the performance of the nanoantennas. An approximate expression resting on modal results is proposed for the resonant length of nanomonopoles, and a simple equivalent circuit, also resting on modal results, but involving transmission lines and a capacitor (modelling the gap) is proposed to determine the resonant wavelength of nanodipoles. The expression and the circuit yield results that are in good agreement with the full computations, and thus will prove useful in the design of nanoantennas.